fix(arcade): prevent empty update in settings API when only gameConfig changes

When only gameConfig is updated (without accessMode, password, or gameName),
the updateData object remained empty, causing Drizzle to throw "No values to set"
error when attempting to update arcade_rooms table.

Now only updates arcade_rooms if there are actual fields to update, preventing
the 500 error while still allowing gameConfig-only updates to room_game_configs table.

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude <noreply@anthropic.com>

apps/web/src/app/api/arcade/rooms/[roomId]/settings/route.ts

@@ -148,12 +148,15 @@ export async function PATCH(req: NextRequest, context: RouteContext) {
       await db.delete(schema.arcadeSessions).where(eq(schema.arcadeSessions.roomId, roomId))
     }
 
-    // Update room settings
-    const [updatedRoom] = await db
-      .update(schema.arcadeRooms)
-      .set(updateData)
-      .where(eq(schema.arcadeRooms.id, roomId))
-      .returning()
+    // Update room settings (only if there's something to update)
+    let updatedRoom = currentRoom
+    if (Object.keys(updateData).length > 0) {
+      ;[updatedRoom] = await db
+        .update(schema.arcadeRooms)
+        .set(updateData)
+        .where(eq(schema.arcadeRooms.id, roomId))
+        .returning()
+    }
 
     // Get aggregated game configs from new table
     const gameConfig = await getAllGameConfigs(roomId)